Augmented Lagrangian finite element methods for contact problems
- 1 January 2019
- journal article
- research article
- Published by EDP Sciences in ESAIM: Mathematical Modelling and Numerical Analysis
- Vol. 53 (1), 173-195
- https://doi.org/10.1051/m2an/2018047
Abstract
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the Signorini problem, where a lateral contact condition is imposed are considered. We consider both continuous and discontinuous approximation spaces for the Lagrange multiplier. In the latter case the method is unstable and a penalty on the jump of the multiplier must be applied for stability. We prove the existence and uniqueness of discrete solutions, best approximation estimates and convergence estimates that are optimal compared to the regularity of the solution.This publication has 32 references indexed in Scilit:
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